Optical mineralogy. Method of the study

Transcription

1 1 Optical mineralogy Primarily aims To learn the language (meaning and dentition of the used terms) of optic and optical mineralogy To Learn some principle of optic such as property of light (polarization, interference, reflection, refraction, dispersion and wave length competent) the definition of the optic sign of uniaxial crystals To Learn the different effects minerals and materials on light under polarizer microscopes (these effects such as index of refraction, double refractions, polarization, inference color and figure Get to learn what is the biaxial and uniaxial indicatrix, its various axes, planes, and the 2V angle. Learn to determine the. Indices of refraction, optic sign, and 2V angle of biaxial crystals in addition to sign of elongation. Final aim: to learn how to identify minerals and the rocks with differentiating their economic values Method of the study The study of mineral are done with thin section under polarized microscopes by and follow the below subdivision: 1- General aspects of minerals: Mineral composition, crystal symmetry, and optics 2- Orthoscopic mode of the mineral study / plane-polarized light: relief and refractive indices, form, cleavage, color 3-Orthoscopic mode of the mineral study / crossed polarizers: birefringence, sign of elongation, extinction, twinning 4- Conoscopic mode of the mineral study: optic character and optic sign, optic axial angle

2 2 Relation of the optical mineralogy with other branches of Mineralogy Mineralogy includes Visual study of hand specimen by eyes Chemical mineralogy Optical mineralogy Minerals Crystal morphology (crystallography) Optical mineralogy: that branch of geological sciences that deal with optical properties of minerals. Optical mineralogy mainly deals with three things: 1- Polarizing microscope (petrographical microscope) 2- Visual light (white light) 3- Thin section 1-polarizing microscope Polarized microscope is of possible interest to many sciences that are concerned with crystalline materials such as : geology, mineralogy, crystallography, materials science, biology, forensic science Polarizing microscope has four differences as compared to ordinary microscope, they are: a) It has rotating circular stage which graduated in to 360 degrees b) It has Polarizer and analyzer plates: In modern microscopes polaroid sheets are used as polarized and analyzer but in old microscopes Nicol prism or Ahern prism are used the polarizer and analyzers used in our microscopes are made of Polaroid sheets which consist of a sheet of cellulose fed with crystals of quinine iodosulfate which is absorbing light in one direction but transmit in the other direction. c) It has Accessory plates : such as mica plate, gypsum plate and quartz wedge d) It has Bertrand lens: located between analyzer and ocular, which brings the image of interference fiure in to the focal plane of the ocular. e) Objectives : they are used for magnification of the original object on the stage, two numbers are engraved on the tube of objective lenses: 1- Magnification of the original object e.g: (1x, 3x, 10 x, 40 x and 100 x) the objective lens in the diagram has magnification power of (10) time more than original object on the stage. 2- Numerical apertures (N.A) N.A = sin u

3 U = angular operator / * N.A = lines separated/ 1 square inch So if N.A = 0.25 it means that lines can be separated in one square inch 3 Free working distance: It is the distance between the objective and the top of the cover glass of the microscopic slide when the objective is focused Comparison of the free working distance, angular apertures and one-half angular aperture (u) for the three types of objective lenses. Ocular: (Huygenian type of ocular) It is used for magnification of the image formed by objective and to bring the image to plane of exist pupil it is consist of field lens, eye lens and fixed diaphram. 1-Parallel pollars Ordinary light composed of various wave lengths 2- cross- polars

4 4 Modern students polarizer microscope (normally used after, 1970) on which the most important parts are indicated (Also called petrographic microscope) Simple polarizer microscope (normally used before, 1970) on which the most important parts are indicated

5 5 Some application of Polaroid sheets (plates) in human life: 1- LCD watches (liquid crystal display watch) Television, mobile, computer and digital watch screens consist of a two Polaroid sheets (one act as polarizer and other as analyzer) which are called LCD (liquid crystal display) sheets or pieces. These sheets are called Polaroid sheets which are first made by Polaroid Company in USA. The most common liquid-crystal displays (LCDs) in use today rely on picture elements, or pixels, formed by liquid-crystal (LC) cells that change the polarization direction of light passing through them in response to an electrical voltage. As the polarization direction changes, more or less of the light is able to pass through a polarizing layer on the face of the display. Change the voltage, and the amount of light is changed. The sheets are consisting of small crystal embedded in certain liquid. as shown in the cross-section diagram in the diagram. when there is no battery in the watch, the watch screen appear clear (bright 1) but when battery used some area of the liquid crystals became dark because the crystals of these area acts as analyzer and absorb light as shown in position. Digital LCD watches work by polarizer and analyzer, the blue (grey) segments are those through which voltage or current is applied changing direction of the polarization of the crystals and black which is visible.

6 6 LCD or Plasma Screens contain two polaroid sheets that are act as polarizer and analyxer 2- Sun glass When sun light strike a polished surface (water surface) a part of this light polarized by reflection and when reaches the glass on the eye, the polarized part absorbed by the glass which made of Polaroid sheet and decrease its effect on the eye.

7 7 Adjustment of polarizing microscope: 1- Centering the objective with the microscope field of view. 2- Crossing the polars (or Nicols) 3- Testing the cross hairs 4- Determination of the vibration plane of the lower polar (polarizer) 1- Centering the objective: The objective is (centered) when its lens axis concede with the vertical axis about which the microscope stage is rotating For centering the objectives a simple procedure is followed: 1- Fined an easily recognized point and then rotate the stage. the point must has a concentric circle of rotating about the intersection of the cross hair but it has no concentric circle of rotation, the following procedure is followed:- 1-rotate the stage until the point is farthest from the intersection of the cross-hairs 2-bring it in half way by means of centering screws 3-then bring it to the center of the cross hairs to the center of the field of view) by actually moving the slide by hand 4-rotate the stage and repeat the operation if the centering has not been completed in the first time 2-Crossing the polars (polarizer and analyzer) Every time before putting the slide on the stage, the polars must be crossed as shown on the page (1 and 2) (cross polars diagram) the polarizer located below the stage which has N-S polarization direction the analyzer located between objective lenses and the ocular which has E.W vibration direction. Which both polarizer and analyzer are inserted in the light path of microscope the field of view become dark this mean that both polars are at right angle to each other 2- Testing the cross hairs: the cross hairs are lines engraved on a glass plate in the ocular. It is important that the hair lines be parallel to the planes of the vibration of the two polars. This is done by the manufacturer company, but some time necessary to test the setting of the cross hairs with planes of the polars. This done by natrolite crystal with elongate and rectangular section. The natrolite crystal becomes dark between crossed polars when the edges of the crystals are parallel to the vibration direction A slide containing a small natrolite crystal may be placed up on the stage between crossed polars. If the cross hairs are in adjustment, the hair lines should be parallel or at right angles to the straight lines of the crystal boundary (crystal of face) 3- Determination of the vibration plane of the lower polar (polarizer) :- After the other adjustments have been made, the vibration direction of the polarizer can be determined with either fibrous tourmaline fragments or a rock section containing biotite showing cleavage. Biolite is used because of availability of biotite. Biolite is brown under polarized light and has maximum dark color when the cleavage is parallel to the vibration of the polarizer. So the stage

8 8 is the rotated until biotite attains maximum dark brown cooler, in this case the direction of the biolite cleavage is direction of polarizer vibration. 2- Visual light (traverse wave motion) The vibration light represent limited band of wave length with in electromagnetic spectrum, ranging from 3900 to 7700 A (angstrom). If light of all wave length simultaneously reach the human eyes, the light is interpreted by the brain as white light. But light with one wave length called mono chromatic light, for example, sodium vapor lamp is a source of mono chromatic light with wave length of 5890 A but the tungsten lamp is a source of white light (ordinary light).traverse wave terminology and shape in which polarization and interference occur. Only sound wave is longitudinal which means that the vibration direction is parallel to direction of propagation in which polarization and interference do not occur 3- Thin section It is a fragment of rock or mineral mechanically reduced to thickness of (0.03mm) by grinding and polishing of thickness makes most rocks and minerals transparent which finally ready for optical study. Procedure for making thin section A thin section is a 30 µm (= 0.03 mm) thick slice of rock attached to a glass slide with epoxy. Typical thin section slides are 26 mm x 46 mm, although larger ones can be produced. They are generally covered by another glass slide, a cover slip also attached to the rock with epoxy. The epoxy ideally has an index of refraction of 1.54, although our epoxy is slightly higher, perhaps The sections may be left uncovered for chemical analysis on the SEM or electron microprobe. If so, temporary cover slips may be weakly attached with glycerin. 1- Sawing a hand specimen to get a flat chip which has 4 square cm in area. 2- Polishing one of the two surfaces and then mounting on glass slide using Canada balsam. 3- Grinding of the chip, which is mounted on the glass slide, to a thickness close to 0.03mm with (1000) grade carborundum. 4- Then the slide covered with thin cover slide by liquid Canada balsam. 5- During polishing the chip must be examined several times under polarizer microscope to determine the standard thickness of the thin section (0.03mm). This done by the interference color of the quartz or feldspar which they give first order grey when the thickness reaches (0.03mm).

9 9 Position (location) of the thin section in the light ray pass from its radiation from the bulb to the eyes of human Position (location) of the thin section in the light ray pass from its radiation from the bulb to the eyes of human PROPERTIES AND NATURE OF LIGHT The study of the following properties of light are necessary for 1- Light represents a relatively limited band of wave lengths within the electromagnetic spectrum, this band ranging from 3900 to 7700 A 2- Light is traversal wave which can undergo 1) interference 2) polarization 3) Reflection 4) refraction 3- Reflection and refraction:- When light passes from air in to a denser medium, such as glass, part of it is reflected from the surface back in to the air and other part enters the glass. The reflected ray obeys the law of reflection which says that: 1- The angle of incident (i) equals the angle of reflection (r), when both angles are measured from the surface normal 2- The incident and reflected rays lie in the same plane. 3- That part of light that passes in to the glass travels with lesser velocity than in air and no longer follows the path of the incident ray but is bent or refracted. The amount of bending depends on the 1) obliquity of the incident ray 2) the relative velocity of light in the two media. The greater the angle of incident, the refraction (small angle of refract angle and the greater the velocity difference, the greater refraction. Speed of light = 3*10 8 m 4- Index of refraction:

10 10 Index of refraction of material can expressed as the ratio between the velocity of light in the air and it is velocity in the denser material n= velocity in air/ velocity in material The velocity of light in air is considered here as equal to the reciprocal of the velocity N=1/v = 1/ velocity of light in materials Generally index of refraction of two substances in contact with each other are n1/n2 = v2/v1 The precise relationship of the angle of incident (i) to the angle of reflection (r) is given by Snells law: which state that ratio of sin I / sin r = constant and this constant is index of refraction (n). { sin i / sin r = n } Which is regarded as constant property for each transparent material. N1/ n2 = 1v1 / 1I v2 n1/ n2 = v1-1 / v2-1 v2/v1

11 11

12 12 5- Dispersion: It is difference in indices of refraction of a given mineral for different wave lengths of the spectrum of white light. The velocity of light in glass is equal to frequency multiplied by wave length, or v = f ë and if we supposed that if (f) is fixed, then the longer (ë) the greater velocity (as for red light ) and violet has smaller (ë ) so has less velocity in the glass. because of reciprocal relation between velocity (v) and refractive index (n), n = 1/ v, so n for red light is less than n for violet light as shown in the diagram above, this is known as dispersion of the indices, and because of it, monochromatic light is used for accurate determination of the refractive index. Dispersion of the minerals = nv nr. The least dispersive mineral is fluorite and the mineral with the highest value of dispersion is diamond Material dispersion can be a desirable or undesirable effect in optical applications. The dispersion of light by glass prisms is used to construct spectrometers and spectroradiometers. Holographic gratings are also used, as they allow more accurate discrimination of wavelengths. However, in lenses, dispersion causes chromatic aberration, an undesired effect that may degrade images in microscopes, telescopes and photographic objectives. The phase velocity, v, of a wave in a given uniform medium is given by Where c is the speed of light in a vacuum and n is the refractive index of the medium. In general, the refractive index is some function of the frequency f of the light, thus n = n(f), or alternatively, with respect to the wave's wavelength n = n(ë). The wavelength dependence of a material's refractive index is usually quantified by an empirical formula, the Cauchy or Sellmeier equations. Total reflection and the critical angle The index of refraction is a fundamental property of a substance, and its determination may provide valuable diagnostic information about minerals and crystals. Over a period of four centuries, widely varying devices and experimental arrangements for measuring indices of refraction have been developed. These instruments are generally called refractometers, or-if the physical phenomenon of total reflection is used--also total reflectometers. These range from the precursor of Kepler's refractometer (1611) to the primitive but ingenious instrument of Wollaston (1802) to modern. When light pass from a lower (n) medium, it refracted away from the surface normal (as shown below) The greater obliquity of incident ray, the greater angle of refraction until the angle reached which the refracted ray is parallel to the surface (E and E - ) in this case the angle of refraction is 90 degree, and the angle of incident, is in this case, called critical angle. So the critical angle is the incident angle at which the refracted angle is 90 degree (the angle between ray- 3-and surface normal ray-1) and at any angle greater than critical angle total reflection will occurs Q1/ why mono chromatic light used for measurement of refractive indices.

13 13 Measurement of refractive index of minerals Refractometer A refractometer is an absolute necessity for gem identification. It measures the refractive index of your gems. Besides the RI, a refractometer will also give you the birefringence and optic sign. When possible, it is easier to obtain the optic sign from a polariscope. However, that can t always be done, so you need the refractometer as an alternate means to determine the optic sign when necessary. Refractometers costs in the neighborhood of $500 to $1000. In North America the primary source is the Gemological Institute of America. In Europe the primary supplier is Kneuss Instruments. Used refractometers occasionally come available on ebay. Inexpensive models are now available from China for under $200. Their reliability varies, so if you purchase one of these make sure it is from a reliable company that will exchange it. For instructions on how to check the accuracy, see Gem Lab Refractometer. Two photos of two jeweler's refractometers as seen from different directions (see the diagram below for parts) showing light reflected at the critical angle (C.A) for mineral spinel

14 14 Ray path illustrating reflection and refraction, Rays 1, 2, 3, are incident from the lower left and each ray has reflected and refracted portion. The angle of the reflection is equal to the angle incidence (ei) can be found by application of the Snells Law. Ray 3 shows the case of the total reflection when èt=90 degrees 1- By refractometer Finding of critical angle is a quick and easy method for determining the refractive index of minerals and liquids. The instrument used is refractometer which consists of a polished hemisphere of high refractive index glass. a crystal face or a polished surface of the mineral is placed on the equilateral plane of the hemisphere but separated from it by a film of a liquid. The liquid must has a refractive index higher than that of hemisphere slightly convergent light is directed up ward through the hemisphere and depending on the angle of incident, is either partly refracted through the unknown mineral or totally reflected back through the hemisphere. If a telescope is placed in a position to receive the reflected ray, we can observe a sharp boundary between the portion of the field intensely illuminated by the totally reflected light and the remainder of the field, when the telescope is moved so that its cross hairs are precisely on the contact, the critical angle C.A is red on the scale on the hemisphere. By knowing this angle and the index of refraction of the hemisphere (n) we can calculate the index of the mineral (n) of the mineral = sin critical angle (n) hemisphere Index of mineral = sin critical angle index of hemisphere n= N critical angle The hemisphere must be made of high index glass of known index. Nr/ni = sin i/ sin r Q1 / why the refractometer does made in the form of hemisphere Q2/ how can you prove that (f) not change when light pass through high density (high n) material.

15 15 Longitudinal section through jeweler's refractometer (see the photo above) showing light reflected at the critical angle (C.A) for mineral spinel 2- By using polarizer microscope This method is called De chaulnes method which permits measurement of refractive index of transparent plates (grains) with only fair accuracy (not as accurate as refractometer method). This method depends on the value of true thickness and value of apparent thickness which can be measured by polarizing microscope. the a apparent thickness represents the apparent depth of the plates bottom surface below its top surface as viewed looking down through the plate and the apparent thickness inversely proportional to refractive index n á 1/app. Thickness The diagram above shows the three steps in the chaulness method by microscope. They are: 1-Focus a medium- power objective (N.A o.25) on the upper surface of a glass slide placed on the microscope stage. 2-Carefully place the plate of unknown index on this glass slide then rack upward (by using the fineadjustment drum only ) until the upper surface of the unknown plate is in sharp focus(see fig.2), then indicate (t) which quall the difference between this second reading on the fine- adjustment drum and that obtained in step (1) 3-Now carefully focus downward through the unknown plate until the upper surface of the supporting glass slide is in sharp focus (see fig -3 ) and indicate apparent thickness (ta) which equals the difference between this fine-drum reading and that obtained in step 1. Then the index of refraction of the unknown plate is n= drum difference in 2 / drum difference in step 3

16 16 Three steps of the de Chaulness method for measuring the refractive index of unknown mineral. The differential reading of drum obtained in step 1 and 3 are respectively proportional to t and ta, so this two value can be substituted directly in the above equation as below N=t/ta this equation can be derived from the fig (4) Tan u = ox/op - and tan è= ox/op and op - = ta so op =t Tan u / tan è = op/op - = t / ta since rays px and xz obey Snells law, so n= sin u / sin è for small angles the ratio of their sins approximately equals that of their tangents, so n= sin u / sin è tan u / sin è = t / ta 3-Finding refractive index by immersion methods This method is one of the most convenient methods of measuring the refractive index of a transparent solid (mineral fragments). This is done by immersing fragments of mineral (or any substance) in a series of liquids of known refractive index. The immersion liquids used should at least span (include) the refractive index range between and at intervals of such sets of immersion liquids are obtainable Commercially or can be prepared in the laboratory. This method depends on the observing the relief of the grains (fragment) in the liquids several grain of unknown (n) of the minerals are prepared and all put on a glass plate. Then each grain immersed in a drop of the known liquid (known index) when the grain cannot distinguished in the liquid, this means that the index of grain is equal to that of the liquid Q1/ why immersion method is more convenient than other method The observation of mineral and liquid is done by microscope if the grains are very small but when the grains are large the observation can be done by eye or hand lens. When a grain immersed in liquid (or oil) there is two possibilities 1- The index of mineral is more than the liquid 2- The index of mineral is less than the liquid. In this case how we can know the right relation between the mineral and liquid? This is done by the beck line method

17 17 Beck line: It is a bright line which separate substances (minerals) of different refractive index and this line can be visible under microscope Beck line method: Beck Line method is done under polarizing microscope for comparing the refraction index of two substances in contact with each other. The two substances may be: 1- Two mineral with common boundary. 2- A mineral and immersion oil or liquid 3- Mineral and Canada balsam which surrounds the mineral in thin section. If these substances have different refractive indices, they are separated by a beck line which moves toward the center of high refractive substance when this stage lowered. But moves away from the substance when the refractive index is less. When the mineral can be seen in the oil it means that two substances have different relief. Relief: it is visibility of outline (boundary), cleavage and surface feature of the mineral in the field of the microscope under (ppl) which depends on the index of refraction. 1- Low relief: has smooth surface and boundary cannot be seen but when analyzer used boundary can be seen. I.R = C.B or IR=OIL e.g: quartz and Canada balsam 2- Moderate relief: boundary and surface can be seen I.R of mineral > I.R of C.B e.g.: Muscovite and Canada balsam 3- High or very high relief: the boundary and cleavage of the Mineral can be seen clearly and the surface of the mineral is Rough. e.g: olivine and C.B or olivine and nepheline. Refractive indices and relief of some common minerals minerals Indices of refraction relief C.B Fluorite N= Low relief Quartz Nº = 1.553, nw = Low relief Calcite Nw = 1.658, ne = High relief (twinkling) Apatite Nw = 1.646, Nº High Grossularite N=1.771 Very high relief (garnet) Sphalerite N = Very high relief Aragonite N = 1.530, nb = N = High relief (twinkling) Opal 1.40 diamond 2.46

18 18 Twinkling: it is changing of relief when the stage (with the mineral) is rotated under (ppl) because of changing of refractive index according to crystallographic axis this is seen clearly in calcite and aragonite. Relief: relief is dependent on refractive index of material. Now we are at the position to complete the immersion method of finding the refractive index of un known mineral or substance. When the mineral immersed in known I.R, then we must observed the boundary of the mineral if boundary can be seen, this mean the I.R are not equal, then the Beck line is used to see whether I.R of the mineral is higher or lower than the oil (or liquid) if higher, then another oil is used for immersion with higher I.R until the mineral cannot be seen in the oil, this mean oil I.R = Min.I.R But if lower than that of the mineral then oil of lower I.R is used until the grain cannot be seen I.C = interference color I.R = index of refraction 6- Polarization of light On the main properties of the light is polarization. It is modification of light so that its vibration directions are restricted to a single plane or in a circular or elliptical pattern. Polarized light is used in polarized microscope for optical analysis of minerals or rocks in thin section. 1- Polarizing by absorption Certain material such as tourmaline crystal and Polaroid sheets permit light to vibrate only in one direction (called polarization direction and absorb light in direction at right angle to direction of polarization. Polarization by Absorption by Polaroid sheet Q1/ why does rough surface not make light polarized. 2- Polarization by double refraction: Before discussion of polarization by double refraction it is necessary to discuss the isotropic and anisotropic crystal and substances. All transparent substances can be divided in to two groups:

19 19 A-Isotropic group: includes 1- noncrystalling substances such as gases, liquids, and glass these are called (amorphous materials) 2-crystals that belong to the isometric (cubic) system. In these material light moves in all directions with equal velocity and hence each isotropic substance s has single refractive index (n) A- Anisotropic substance: Which include all crystals, except those of isometric system, the anisotropic crystals are belonging to one of these systems:- 1- Orthorhombic 2- tetragonal, 3- hexagonal 4- trigonal 5- monoclinic and 6- triclinic system. In these crystals velocity of light varies with crystallographic direction and thus there is a range of refractive index. In general, light pas through anisotropic crystal is broken in to two polarized rays vibrating in mutually perpendicular planes. Thus for a given orientation, a crystal has two indices of refraction, one associated with each polarized ray. Now we are in position to discuss polarization by double refraction. Polarization by double refraction was the method by which the first efficient polarizer is made by William Nicol, and this polarizer called Nicol prism, as shown in the diagram, which made of clear calcite crystal called Iceland spar. An elongate rhombohedral crystal cut at a certain angle and then the halves are rejoined by Canada balsam. When light enter the prism from below, it resolved in to two ray o- ray (ordinary ray) and E- ray (extra ordinary ray). Because of the greater refraction of the O- ray it is totally reflected of the Canada balsam surface. The E- ray with refractive index (n) close to that of the Canada balsam continue to pass the prism and emerge as a plane polarized light (PPL). Nicol prism was the only polarizing device in the old microscope but now Polaroid sheets are used. Nicol prism used as polarizer and Analyzer device in old microscopes (before, 1970).

20 20 3-polarization by reflection: Light reflected from a smooth, non metalic surface is partially polarized with vibration direction parallel to the reflecting surface is the degree of polarization depends on the 1- angle of incident, 2- index of refraction of the reflecting surface. The maximum polarization happens When the angle between the reflected and refracted ray is (90) degree this is called (Brewsters law). The fact that the reflected light is polarized can be easily shown by viewing it through a polarizing sheet. When the vibration direction of the sheet is parallel to the reflecting surface the light pass through the sheet with only slight reduction in intensity but when the sheet is turned 90 only small percentage of light reach the eye and all absorbed. Brewster's angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectly transmitted through a surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. This special angle of incidence is named after the Scottish physicist, Sir David Brewster ( ).

21 21 Polarization by reflection from polished surface Polarization by reflection from polished surface (in this case surface of water of Sarchinar pond is used) Q1/ how do you can know that reflected light from smooth surface is polarized. Procedure for optical study of minerals using polarizing microscope in progressive steps A- Under plane polarized light (PPL) 1- Transparency : the ability ( by percent) of minerals to transmit light Transparent Mineral Under PPL and X.P b- opaque minerals ( when transparency is zero and black e.g: hematite, pyrite

22 22 When transparency is more than zero and admit light to pass through. e.g: Quartz, garnet, tourmaline 2- color: it is he color showed by mineral under (PPL). Some time called body color a- Colorless (e.g : quartz, orthoclase, olivine ) b- Colored 1- Nonpleochroic { it means that mineral has body color but non pleochroic e.g:spinel green 2- Pleochroic It means that the color of the mineral changes when the stage is rotated. e.g: Biotite Hornblende pleochroic from brown to pale brown pleochroic from green to colorless 3-Form (or shape) a) Form of crystals Columnar Plagioclase. Euhedral Garnet. andalusite Acicular Subhedral Lath like Kyanite, Aragonite, Equant Grains anhedral Quartz Orthoclase, B-Form of crystals or grains aggregates! Graphic intergrowth Quartz, feldspar Foliated Biotite, muscovite Radiate Chalcedony prehnite Fibrous Chlorite Gypsum Acicular Aragonite Granular e.g: quartz

23 23 C-Form of structure formed by grains and crystals 4-index of refraction (n):- it is\the ratio of velocity of light in air to he velocity of light in contain medium. in thin section study,index of refraction of minerals are compared to index of Canada balsam ( C.B ) or by comparing two minerals which are in contact with each other and one of the two it is index is known. The comparing is done by focusing the microscope on certain grain bounded by C.B then the stage is lowered (or th tube is raised) to see the movement of the bright line which called Becke line, when ( x10 )or (x25) objective is used the line can be seen better than with (x3 ) or (x6) a) Nm < n C.B b) nm > n C.B When the stage lowered the Becke line move to out of the grain, it means that When the stage lowered the B.L moves to center of the grain, it means that Nm> n C.B Nm < n C.B C hm = ncb:- the grain boundary cannot be seen under polarizer because relief of the two substance are equal. To see the grain boundary use analyzer Index C.B = Index of quartz = Relief (contrast): it is the visibility of outline (boundary) and surface of grains of minerals in the field of microscope under (ppl) which depends on the difference between the nm and n c. b or between two minerals with common boundary. a- Low relief: when the mineral has smooth surface and boundary cannot be seen. (to see use analyzer) e.g : quartz, sanidine nm = n C.B b- Moderate relief : boundary and surface can be seen e.g: muscovite, sillimanite nm > n C.B C- High or very high relief: the mineral grain or (crystal) has dark boundary and rough surface e.g: olivine, garnet nm>> Nc.b D-Negative relief: boundary can be seen clearly but the mineral has smooth surface. in this case the mineral seen as a hole in the surrounding mineral e.g: quartz in biolite Quartz in calcite Quartz in garnet 6-Surface nature: a- Smooth surface as quartz (low relief ) b- Moderate rough as feldspar(moderate) c- Very rough surface (high relief) as olivine garnet

24 24 How we can able to see cleavage clearly: 1- The illumination (light) must be lowered 2- The stage must be rotated because cleavage may be visible in one position of the stage and not in others this property of minerals called twinkling as seen in calcite 3- In some case the cleavage\e may be seen better if the focus is changed (to make out of focus) 8- fracture: it is random and irregular breakage of crystals and grains. Properties of minerals under (X.P) of parallel light (now analyzer is used) 9- Anisotropism a) Isotropic minerals: are those minerals which appear dark (black) under (X.P) and remain black when the stage is rotated. e.g: garnet,leucite, Canada balsam also isotropic which can be identified by it is darkness under (X.P) and show no granular nature and has low relief b) Anisotropic minerals: are those minerals, some of which are dark and others are bright under (X.P), and when the stage is rotated successive brightness and darkness (extinction) occurs. 10- Interference color (normal interference color) It is the color displayed by an isotropic crystals under (X.P) light, which formed by retardation of the mineral and absorption by analyzer. The type of color depend on 1- Thickness of the mineral 2- orientation of the crystal 3- Nature of light used 4- type of minerals The normal interference colors are divided in to several orders according to repetition of the certain colors such as: 1 st order, 2 nd order, 3 rd order and 4 th order.etc. and these order arranged according to retardation as one axis and thickness as the other axis, in the form of a chart called interference color chart on which most of the anisotropic mineral are plotted on it

25 25 Mitchel Lievy color chart shows how interference color changes with thickness and with type of mineral Mitchel Lievy color chart shows how interference color changes with thickness and with type of mineral

26 26 Interference color chart of the transparent minerals n2- n1 = birefringence, therefore the retardation = t (n2-n1) = Retardation n2= greatest index T= thickness of a thin section n1= least index The interference color chart is the graphical representation of equation = t (n2-n1) and the light used is white light. Because the maximum value of birefringence (n2-n1) is a constant for each mineral = t for quartz, = t for calcite thus for each mineral there can be plotted a straight line that relates birefringence to thickness of the crystals. By showing retardation ( ) and type of I.C and it is order. Anomalous interference color: it is abnormal production of (I.C) which do not follow the color chart or do not follow the equation = t (n2-n1)}. This type of interference colors (I.C) result from 1- Strong selective absorption of particular wave length during it is passage through the crystal 2- Large variation in the value of the (º and w) for different wave length of light e.g: a mineral has 200 mu retardation gives first order white I.C but for a mineral with an anomalous I.C gives other color. Vesuvianite gray - green Zoisite greenish blue Melielite Berlin blue Masked I.C: it is a mixture of color of mineral (body color) and i.c. In some case the color of mineral covers (masks) the I.C. e.g : staurolite has pale brown under (x.p)which is mixture of pale yellow + first order red. Hornblende masked i.c. glauconite mask i.c Extinction angle: it is the angle through which a crystal (grain) of an isotropic mineral must be rotated froma known cleavage direction (or known crystal face) to the position at which gives maximum extinction (darkness) under (X.P). But if a mineral grain remains in darkness for complete rotation, it means that the section is cut at right angle to optic axis. a) Parallel extinction : It is a type of extinction of birefringent mineral which become dark when direction of cleavages or (crystal face) is parallel to direction of polarizer or analyzer e.g: sillimanite, biolite b) Oblique extinction : in this case the mineral become dark (extinct) when the cleavage make an angle with polarizer or analyzer e.g: amphibole minerals, and pyroxene minerals. Measurement of angle of extinction 1-Find a crystal which has clear cleavage or has crystal boundary. 2-Bring the cleavage direction to be parallel to polarizer vibration direction by rotating the stage. Record the reading value on the stage.

27 27 3-Now again rotate the stage until maximum darkness reached for the crystal. Then again record the value of the angle on the stage. The subtraction of the two values is equal to angle of extinction Second reading first reading = angle of extinction The stage rotated to the left and right and we must take the nearer side c) Symmetrical extinction: this type of the extinction appears in a number of minerals with rhombic cross-section of the crystals. These crystals become dark under (X.P) when the vibration direction of polarizer are parallel to diagonal of the rhombic crystal d) Wavy extinction: this type of extinction occurs when the crystals extinguish successively in adjacent area as the stage is rotated. This type of extinction formed because of pressure which causes the change of optic axis direction. Sign of elongation it is indication of vibration direction of elongated crystals (lath like, columnar& needle like crystals). When the vibration direction of slow ray of the crystal is parallel to long direction of crystal, the mineral has positive elongation or length slow but when the vibration direction of slow ray lies across the crystal in the short direction the mineral has negative elongation or length fast this properties is determined by using accessory plate called gypsum plate which marked with vibration direction of slow ray & fast ray. Finding of the sign of elongation is as following: 1- Find elongate crystal 2- Bring the crystal to 4 quadrant and align it to be parallel to direction of inserting the gypsum plate and to has maximum (I.C) 3- Insert the gypsum plate and see whether the (i.c) of the mineral increase or decrease. Because vibration direction of slow and fast ray are indicated on the gypsum plate so we can make comparison between that of the mineral and that of gypsum plate 4- When the i.c. increase it means that slow direction of gypsum plate coincide (or parallel) to that of the mineral so the mineral has length fast or negative sign of on positive sign of elongation twining : twining is recognized under ( x. p ) by rotating the stage shows grains made up of two or more parts united (joined) along straight line. and when the stage rotated apart extinguish while the other part shows interference color ( by light position )and this is called simple twin which consist of two equal part united along straight line eg : sanidine

28 28 The figure shows the indication of the sign of elongation of crystals by gypsum plate Lamellar twin (poly synthetic twin) This type of twin consist of two alternate bands (lamelate) the first band is in extinction, the second will be in bright position (i.c) and when the stage is rotated the two bands reversed in extinction. e.g: plagioclase, calcite How we can measure the angle of extinction of lamellar twin: By measuring of angle of extinction of this type of twin we can know the minerals of plagioclase group by plotting the value on the curve of Mitchel Lievy as following: Only nearer side is taken 1-Bring the grain that shows lamellar twin to position to be parallel to pol. Vibration direction (uniform illumination position and record the value 2-Rotate the stage to the right until one band become totally dark (extraction position) and record the value 3-The subtraction of the two value will be right side twin extinction angle. 4-Then again bring the grain to the position to be parallel to pol. Vibration direction again. 5-Rotate the stage to the left until the other band of the twin become totally dark then record the value on the stage. The subtraction of the two values will be the angle of left side twin then the two angles divided by (2) which gives us extinction angle of plagioclase then plotted on the curve to know the mineral.

29 29 Indicatrix (which means indices indicator) Definition: it is geometric figure that represent the refractive indices of a crystal. it I s formed by drawing, from central point representing the center of the crystal, lines in all directions whose lengths represent the refractive indices for those vibration direction s. indicatrix is useful for 1-Interpretation of optical phenomena 2-Remembering and predicting of these optical properties, especially for anisotropic minerals. How indicatrix is made by using PPL light 1- Finding refractive indices of the crystal from all direction with indication of value of the angle 2- Plotting of the value of refractive indices on the graph paper with proper scale provided that the angle of plotting is at right angle to angle of measurement. and all the value represented as a straight line drawn from a common point which is coincides with the center of the indicatrix.( center of crystals) 3- Connecting the end of all the lines will give us the indicatrix of the mineral 1- Isotropic indicatrix: the isotropic substance which mentioned before, their indices of refraction do not change with the vibration direction of the light. Consequently, all the vectors relating index of refraction to vibration direction is of equal length, so all isotropic indicatrix are perfect spheres. Radius 1 =2 = 3 = 4 = 5 are equal in length 2- An isotropic indicatrix : in an isotropic media the index of refraction actually varies according to the vibration of the light in the crystal, so the indicatrix for anisotropic minerals is divided in to two types ; Uniaxial and biaxial optical indicatrix. a- Uniaxial indicatrix : Type equation here. The mineral of the trigonal, hexagonal and tetragonal have the uniaxial indicatrix which is not a sphere but an ellipsoid of rotation. This means that the light vibrates parallel to optic axis has an index called (nº) (epsilon). But for all vibration direction at 90 degree to the optic axis (coincides with c- axis) the crystal has other index which symbolized (nw) (omega). all value of (n) between º and nw are intermediate in value between the two and symbolized º - (epsilon dash) and its value change with the angle è which can be calculated by this equation when (Nº) and (nw) are known N º - = nw/ -1 )cos 2 ètype equation here. When the value of nº is greater than w the crystal is positive?(uniaxial positive) nº w = positive e.g : quartz But when nw is greater than nº the crystal has negative sign or (uniaxial negative) nº w = negative e.g: calcite optical

30 30 Left: Indicatrix of a positive uniaxial mineral nå > nù which has only two indices (they are called Omega ù (smaller) and Epsilon å (larger). Right: Indicatrix of a negative uniaxial mineral (nå < nù) which has only two indices (they are called Omega ù (larger) and Epsilon å (smaller). Q/ why uniaxial crystals have two indices (two axes)? Left: A quartz crystal (optically uniaxial crystal) in which its Indicatrix is drawn inside it can be seen that it has two refractive indices. Right: optically isotropical mineral (appear dark under XP light) it can be seen that it has only one index (such as garnet or glass)

31 31 Indicatrix of isotropic mineral, is perfect sphere which means that indices don t change according to direction Two uniaxial crystals and their indicatrix

32 32 Biaxial indicatrix: Orthorhombic, monoclinic and triclinic crystals are called optically because they have two directions in which light travels with zero birefringence (has no double refraction ) but in uniaxial crystals there is only one such direction. Light moving through a biaxial crystal (except along the optic axes) travels as two rays with mutually perpendicular vibrations. The velocities of the rays differ from each other and change with changing crystallographic direction The vibration direction of the fast ray is X, = = = = slowest ray is Z, This two vibration direction are at right angle to each other. The direction perpendicular to the plane defined by X and Z is designated as Y. For biaxial crystals there are thus three indices of refraction resulting from rays vibrating in each of these principal optical direction. The numerical difference between the greatest and least refractive indices is the birefringence = n2-n1. The following letters and symbols have been used to designated the refractive indices, Index direction ray velocity (alpha) n á X highest (Beta) nâ Y Intermediate (Gama) nä Z Lowest The biaxial indicatrix is a triaxial ellipsoid with three axes X, Y and Z are optical directions and they are mutually perpendicular. The lengths of the semiaxes are proportional to the refractive indices n á along X, nâ along Y and nä along Z. The figure at right shows the three principal sections through the indicatrix, these are the planes XY, YZ, and XZ.

33 33 They are all ellipses and each has the length of it is semimajor and semiminor axes proportional to refractive indices as shown. The most important section is the XZ section. with it is semimajor axes proportional to n(gama) and it is semiminor axis proportional to n á, there must be points on the ellipse between these extremes where the radius is proportional to the intermediate index, nâ(beta). With two exceptions is circular section of which S is the radius. The two directions normal to these sections are the optic axis, and the XZ plane in which they lie is called the optic plane. The Y direction perpendicular to this plane is the optic normal. Light moving along the optic axis and vibrating in the circular sections shows no constant refractive index. When nâ(beta ) is close to ná (alpha), the circular sections make only a small angle with the XY plane (section) and the optic axes make the same angle with the Z direction. The angle between the two optic axes, known as optic angle and is equal to (2v). The optic angle is always acute and when bisected by Z, Z is acute bisectrix (Bxa), and X is obtuse bisectrix (BXO) because it bisects the obtuse angle between the optic axes when Z is the Bxa the crystal is optically positive. If nâ(beta ) Is closer to nä than to n á(alpha) the acute angle between the optic angle between the optic axes is bisected by X and the obtuse angle bisected by Z. In this case X is acute bisectrix Bxa, and the crystal is negative when the nâ lies exactly half way between á and ä, the optic axis is 90 degree The principal sections of the biaxial indicatrix: XZ section, YZ section, YX section. The space axes (X, Y and Z) are important as references axes for learning indicatrix and optical mineralogy because they are fixed so the maximum, intermediate and minimum indices of biaxial minerals are measured along the axes). See that that ná (alpha), nâ (beta) and nä (Gamma) are measured along X, Y and Z in biaxial minerals.

34 34 Different important components of the positive and negative biaxial indicatrix, each of the two circular sections (blue) are perpendicular to one of the optic axis. The two 2V is the smallest angle between the two optic axes in biaxial crystals. In positive indicatrix Z is BXa and X BXo while in negative is BXa is X and BXo is Z.

35 35 Different important components of the positive biaxial indicatrix, each of the two circular sections (yellow and blue) are perpendicular to one of the optic axis. The two 2V is the smallest angle between the two optic axes in biaxial crystals.

36 36 Same sections as shown above but we called it looking down through nâ (beta) of the biaxial indicatrix and you see the two optic axes (OA) in blue color and the trace of the circular section is in green. INTERFERENCE OF LIGHT Two light interfere when the following conditions are available: 1- Must have one source 2- Must have the same ë(wave length) or must be monochromatic 3- Must have the same line phase (retardation) must be (ë, 2 ë, 3 ë, etc.) Destructive interference between two waves with phase difference of ë ½ ë, 3/2 ë, 5/2 ë, etc) Constructive interference Interference of two waves with phase difference of n ë (1 ë, 2 ë, 3 ë) The figure below shows interference of light from two slit illuminated by one source of light, interference occurs when the phase difference is equal to whole number of wave length Interference color:

37 37 a) Interference color formed by reflection from a thin layer of oil floating on water. This formed by interference of two light waves reflected at opposite surfaces of the thin films of oil. In case of thin film (layer) interference occurs if phase difference is whole number (1 ë, 2 ë, 3 ë etc)but the path difference of the light enter the layer must be (1/2 ë ) or 2 ray + 3 ray = 1/2 ë and the light reflected from the upper surface (ray 1) undergo reversal of phase of 1/2 ë so the phase difference of ray (4) is 1 ë,2 ë,3 ë etc as compared to ray (1) Phase difference (P) = 1/2 ë by reversal of ray (1) + ½ ë by pass difference = 1 ë In the case of this layer the conditions for constructive interference are available.why? 1- The light has one source 2- The thickness make the light to be similar to mono chromatic light because permit certain wave length to interfere only depending on the thickness of the layer. 3- The phase difference is the whole number (ë,2 ë,3 ë ) Interference color formed under polarized microscope by isotropic minerals. Condition for this type of interference color 1- The polars must be crossed(analyzer is used) 2- The mineral crystal must be at 45 degree from extinction 3- The phase difference must be ½ ë, or ( ë). N=0, 1, 2, 3.etc. 4- When ordinary light leaves the polarizer and vibrate perpendicular to the paper (see the figure), and when strike the lower surface of the mineral section, the ray broken in to two rays. Both rays are polarized, but at right angle and the two ray travel at different velocities in the mineral along each plane,as a result, When the two rays emerge on the upper surface of the mineral, one has travel farther than the other. Both continue along a straight line to the analyzer and vibrate at a right angle to each other. When they reach analyzer the two rays are resolved to a single plane as indicated in the figure. Thus the two rays come out from upper surface of the analyzer vibrate in the same plane which they are in the same phase caused by the mineral. So when the phase difference is ½ ë interference color between the two rays and certain color can be seen which called interference color Caused by constructive interference. Destructive interference: Destructive interference occurs for those wave lengths which hove n ë retardation during moving through mineral grain and the resultant (R) is equal to zero but other wavelengths will undergo retardation of ½ ë and constructive interference will occur. Retardation ( ): for one mineral ( ) may be changed through wide range by: 1- Varying the thickness (t) of the mineral 2- Changing orientation of the mineral section in such away as to change the indices of refraction n1 and n2 of the two rays emerging from the mineral. this relationship may be expressed the equation